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This study presents methane-air counterflow simulations, in computationally efficient similar form, allowing combustible mixtures to flow from one or both directions in order to learn more about multi-branched propagating flame structures (e.g., a triple flame). These structures with both premixed and non-premixed flames are commonly seen in more practical combustion analyses. A range of realistic mass mixture fractions and asymmetric chemical rate laws are examined while avoiding the commonly forced unreal symmetric behavior with one-step second-order kinetics. Moreover, a survey of critical parameters is performed varying pressure and normal strain rate to define the flame structure and detect different characters. Three flames can co-exist if the strain rate is low enough and the pressure is high enough. However, at higher strain rate and/or lower pressure, only one or two flames might be obtained. Negative regions of heat release rate are observed and linked to potential endothermic reactions. With a rich premixed mixture at low strain rates and pressures, high exothermic reactions producing CO$_2$ and H$_2$O, and consuming CO and H$_2$ causes a heat-release-rate peak. Unexpected character of the lean and rich premixed flames is observed, leading to the conclusion that these flames are diffusion-controlled.